Recent contributions to Implementation/Mechanism Design Theory. E. Maskin. Mechanism Design/Implementation. part of economic theory devoted to “reverse engineering” usually we take mechanism, game, or economy as given try to predict the outcomes it generates in equilibrium
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Recent contributions toImplementation/Mechanism Design Theory
technologies, endowments, etc.)
social choice function
mechanism implements SCF
O. Lange and A. Lerner: yes
L. von Mises and F. von Hayek: no
Formal mechanism-design theory dates from
Since then, field has expanded dramatically
possible outcomes abstract set of social alternatives
(at least 10 major survey articles and books in last dozen years or so)
design of bilateral contracts between buyer and seller
(several recent books on contract theory, including Bolton-Dewatripont (2005) and Laffont-Martimort (2002))
design of auctions for allocating a good among competing bidders
(several recent books - - Krishna (2002), Milgrom (2004), Klemperer (2004))
(to buyer who values good the most)
i.e., how to implement SCF that selects efficient allocation
In private values case (each buyer’s valuation is independent of others’ information),
Vickrey (1961) answered question:
then, in equilibrium buyer i with signal bids true contingent valuation:
Robust Mechanism Design
auction in which buyer i bids is “robust” or “independent of detail” in sense that
regardless of i’s belief about
(remains equilibrium even if iknows )
Why is robustness important?
set of possible types set of possible preferences
in auction model above, if signals correlated, auctioneer can attain
efficiency and extract all buyer surplus, even without conditions such as
(Crémer and McLean (1985))
Given SCF , can we find mechanism for which, regardless of type space associated with preference space , there always exists f-optimal equilibrium?
(robust partial implementation)
But ex post partial implementability is necessary for robust partial implementation if
agent i cares just about
equivalently: for all for which
there exist i and such that
analogous condition for Bayesian implementation (agents have incomplete information)
- - Postlewaite and Schmeidler (1986), Palfrey and Srivastava (1989), Jackson (1991)
for all and
there exist i and a such that
implementable by mechanism such that, regardless of type space associated with Θ, all equilibria are f-optimal
for all there exists
Example (Jackson and Srivastava (1996))
(1) Implications of ex post monotonicity and robust monotonicity for applications
(2) implications of other sorts of uncertainty for implementability
Indescribable States, Renegotiation and Incomplete Contracts
(i.e., on mechanism design)
Nevertheless, we have:
If parties are risk averse and can assign probability distribution to their future payoffs, then can achieve same expected payoffs as with fully contingent contract (even though cannot describe possible states in advance)
can design mechanism to ensure incentive compatibility
Where does risk aversion come in?
Answer: helps with incentive compatibility
but 1 plays
then not clear from who has deviated
But what if parties can renegotiate outcome ex post ?
Why isn’t randomization renegotiated away?
How to provide fully satisfactory foundation for incomplete contracts?